Energy drift

In LN, the bonded interactions are treated by the approximate linearization, and the local nonbonded interactions, as well as the nonlocal interactions, are treated by constant extrapolation over longer intervals Atm and At, respectively). We define the integers fci,fc2 > 1 by their relation to the different timesteps as Atm — At and At = 2 Atm- This extrapolation as used in LN contrasts the modern impulse MTS methods which only add the contribution of the slow forces at the time of their evaluation. The impulse treatment makes the methods symplectic, but limits the outermost timestep due to resonance (see figures comparing LN to impulse-MTS behavior as the outer timestep is increased in [88]). In fact, the early versions of MTS methods for MD relied on extrapolation and were abandoned because of a notable energy drift. This drift is avoided by the phenomenological, stochastic terms in LN. 

The heightened appreciation of resonance problems, in particular, has been quite recent [63, 62], and contrasts the more systematic error associated with numerical stability that grows systematically with the discretization size. Ironically, resonance artifacts are worse in the modern impulse multiple-timestep methods, formulated to be symplectic and reversible the earlier extrapolative variants were abandoned due to energy drifts. 

Organisms that use infrared photosynthesis as an accessory source of energy drift away from the hydrothermal system. Here they become fully dependent upon photosynthesis. 

The molecular dynamics simulation is performed using the MOTECC suite of programs (Sciortino, Corongiu and dementi, 1994) in the context of microcanonical statistical ensemble. The system considered is a cube with periodic boundary conditions, which contains 343 water molecules. Compatibility of this data with the water experimental density of0.998 g/cm requires a cube with a side length of 21.7446 A. In accordance with the polarizable model, a spherical cutoff with radium equal to half of the simulation cube side is imposed, together with a switching function to suppress energy drift. 

Minimize real-space evaluation in Ewald summation Sagui et al. have quantified the impact of the real-space cutoff used in their MTP Ewald implementation on the energy drift of a constant-energy simulation [54]. Restricting the real-space evaluation to a minimal amount and performing the rest in reciprocal space can lead to significant improvements. The authors showed minimal energy and force errors down to 4.25 A of direct interaction cutoff. They report an increase in computational time due to MTP interactions of only 8.5 with respect to simple PCs. 

Fig. 3.9 The radial distribution computed using the explicit 4th order Runge-Kutta method with stepsizEs of ft = 0.01 and ft = 0.02. Due to energy drift, the ft = 0.02 solution is completely inaccurate, whereas even the ft = 0.01 curve is much worse than that obtained using Verlet with ft = 0.02, despite the fact that the Runge-Kutta method uses four times the number of force evaluations per timestep. These calculations were performed using IM timesteps if a longer simulation were used, the RK4 errors in distribution would be expected to increase (due to the increasing energy drift) whereas the errors reported in Figure 3.6 for the Verlet method would not be expected to depend appreciably on the time interval...

A number of methods have been proposed to overcome the MTS barrier, including averaging methods that mollify the impulse, allowing time steps of up to 6fs while maintaining the favorably small energy drift attained by impulse MTS methods with 4fs time steps. We will omit here the details of these time-stepping algorithms but point to a reference that explicitly provides implementation details. 

Temperature, average 118, 122 Temperature fluctuation 117, 119, 121 Thermodynamic limit 84 Thermostat algorithm 112 Thermostats 120-138 energy drift 120,126... 

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